Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.

Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping

This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

Functional genes and gene array analysis as tools for monitoring hydrocarbon biodegradation

Bioremediation, which is the exploitation of the intrinsic ability of environmental microbes to degrade and remove harmful compounds from nature, is considered to be an environmentally sustainable and cost-effective means for environmental clean-up. However, a comprehensive understanding of the biodegradation potential of microbial communities and their response to decontamination measures is required for the effective management of bioremediation processes. In this thesis, the potential to use hydrocarbon-degradative genes as indicators of aerobic hydrocarbon biodegradation was investigated. Small-scale functional gene macro- and microarrays targeting aliphatic, monoaromatic and low molecular weight polyaromatic hydrocarbon biodegradation were developed in order to simultaneously monitor the biodegradation of mixtures of hydrocarbons. The validity of the array analysis in monitoring hydrocarbon biodegradation was evaluated in microcosm studies and field-scale bioremediation processes by comparing the hybridization signal intensities to hydrocarbon mineralization, real-time polymerase chain reaction (PCR), dot blot hybridization and both chemical and microbiological monitoring data. The results obtained by real-time PCR, dot blot hybridization and gene array analysis were in good agreement with hydrocarbon biodegradation in laboratory-scale microcosms. Mineralization of several hydrocarbons could be monitored simultaneously using gene array analysis. In the field-scale bioremediation processes, the detection and enumeration of hydrocarbon-degradative genes provided important additional information for process optimization and design. In creosote-contaminated groundwater, gene array analysis demonstrated that the aerobic biodegradation potential that was present at the site, but restrained under the oxygen-limited conditions, could be successfully stimulated with aeration and nutrient infiltration. During ex situ bioremediation of diesel oil- and lubrication oil-contaminated soil, the functional gene array analysis revealed inefficient hydrocarbon biodegradation, caused by poor aeration during composting. The functional gene array specifically detected upper and lower biodegradation pathways required for complete mineralization of hydrocarbons. Bacteria representing 1 % of the microbial community could be detected without prior PCR amplification. Molecular biological monitoring methods based on functional genes provide powerful tools for the development of more efficient remediation processes. The parallel detection of several functional genes using functional gene array analysis is an especially promising tool for monitoring the biodegradation of mixtures of hydrocarbons.

High Resolution Surface Imaging Using a Carbon Nanotube Array with Pointed Height distribution

In this paper we discuss a new technique to image the surfaces of metallic substrates using field emission from a pointed array of carbon nanotubes (CNTs). We consider a pointed height distribution of the CNT array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The CNT array on a metallic substrate is considered as the cathode and the test substrate as the anode. Scanning the test Substrate with the cathode reveals that the field emission current is highly sensitive to the surface features with nanometer resolution. Surface features of semi-circular, triangular and rectangular geometries (projections and grooves) are considered for simulation. This surface scanning/mapping technique can be applied for surface roughness measurements with nanoscale accuracy. micro/nano damage detection, high precision displacement sensors, vibrometers and accelerometers. among other applications.

Design Optimization of Field Emission From A Stacked Carbon Nanotube Array

Fluctuation of field emission in carbon nanotubes (CNTs) is riot desirable in many applications and the design of biomedical x-ray devices is one of them. In these applications, it is of great importance to have precise control of electron beams over multiple spatio-temporal scales. In this paper, a new design is proposed in order to optimize the field emission performance of CNT arrays. A diode configuration is used for analysis, where arrays of CNTs act as cathode. The results indicate that the linear height distribution of CNTs, as proposed in this study, shows more stable performance than the conventionally used unifrom distribution.

Chemically Programmed Ultrahigh Density Two-Dimensional Semiconductor Superlattice Array

Designing an ultrahigh density linear superlattice array consisting of periodic blocks of different semiconductors in the strong confinement regime via a direct synthetic route remains an unachieved challenge in nanotechnology. We report a general synthesis route for the formulation of a large-area ultrahigh density superlattice array that involves adjoining multiple units of ZnS rods by prolate US particles at the tips. A single one-dimensional wire is 300-500 nm long and consists of periodic quantum wells with a barrier width of 5 nm provided by ZnS and a well width of 1-2 nm provided by CdS, defining a superlattice structure. The synthesis route allows for tailoring of ultranarrow laserlike emissions (fwhm approximate to 125 meV) originating from strong interwell energy dispersion along with control of the width, pitch, and registry of the superlattice assembly. Such an exceptional high-density superlattice array could form the basis of ultrahigh density memories in addition to offering opportunities for technological advancement in conventional heterojunction-based device applications.

Field Flow Sensitive Pointer and Escape Analysis for Java Using Heap Array SSA

Context sensitive pointer analyses based on Whaley and Lam’s bddbddb system have been shown to scale to large Java programs. We provide a technique to incorporate flow sensitivity for Java fields into one such analysis and obtain an escape analysis based on it. First, we express an intraprocedural field flow sensitive analysis, using Fink et al.’s Heap Array SSA form in Datalog. We then extend this analysis interprocedurally by introducing two new φ functions for Heap Array SSA Form and adding deduction rules corresponding to them. Adding a few more rules gives us an escape analysis. We describe two types of field flow sensitivity: partial (PFFS) and full (FFFS), the former without strong updates to fields and the latter with strong updates. We compare these analyses with two different (field flow insensitive) versions of Whaley-Lam analysis: one of which is flow sensitive for locals (FS) and the other, flow insensitive for locals (FIS). We have implemented this analysis on the bddbddb system while using the SOOT open source framework as a front end. We have run our analysis on a set of 15 Java programs. Our experimental results show that the time taken by our field flow sensitive analyses is comparable to that of the field flow insensitive versions while doing much better in some cases. Our PFFS analysis achieves average reductions of about 23% and 30% in the size of the points-to sets at load and store statements respectively and discovers 71% more “caller-captured” objects than FIS.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Sampled longest common prefix array

When augmented with the longest common prefix (LCP) array and some other structures, the suffix array can solve many string processing problems in optimal time and space. A compressed representation of the LCP array is also one of the main building blocks in many compressed suffix tree proposals. In this paper, we describe a new compressed LCP representation: the sampled LCP array. We show that when used with a compressed suffix array (CSA), the sampled LCP array often offers better time/space trade-offs than the existing alternatives. We also show how to construct the compressed representations of the LCP array directly from a CSA

Array-based gene expression, CGH and tissue data defines a 12q24 gain in neuroblastic tumors with prognostic implication

Neuroblastoma has successfully served as a model system for the identification of neuroectoderm-derived oncogenes. However, in spite of various efforts, only a few clinically useful prognostic markers have been found. Here, we present a framework, which integrates DNA, RNA and tissue data to identify and prioritize genetic events that represent clinically relevant new therapeutic targets and prognostic biomarkers for neuroblastoma.

A Wavelet based Teager Energy Operator for Spike Detection in Microelectrode Array Recordings

Spike detection in neural recordings is the initial step in the creation of brain machine interfaces. The Teager energy operator (TEO) treats a spike as an increase in the `local' energy and detects this increase. The performance of TEO in detecting action potential spikes suffers due to its sensitivity to the frequency of spikes in the presence of noise which is present in microelectrode array (MEA) recordings. The multiresolution TEO (mTEO) method overcomes this shortcoming of the TEO by tuning the parameter k to an optimal value m so as to match to frequency of the spike. In this paper, we present an algorithm for the mTEO using the multiresolution structure of wavelets along with inbuilt lowpass filtering of the subband signals. The algorithm is efficient and can be implemented for real-time processing of neural signals for spike detection. The performance of the algorithm is tested on a simulated neural signal with 10 spike templates obtained from [14]. The background noise is modeled as a colored Gaussian random process. Using the noise standard deviation and autocorrelation functions obtained from recorded data, background noise was simulated by an autoregressive (AR(5)) filter. The simulations show a spike detection accuracy of 90%and above with less than 5% false positives at an SNR of 2.35 dB as compared to 80% accuracy and 10% false positives reported [6] on simulated neural signals.